Information on Result #1713360
Digital (58, 73, 615)-net over F3, using net defined by OOA based on linear OOA(373, 615, F3, 20, 15) (dual of [(615, 20), 12227, 16]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(373, 1231, F3, 4, 15) (dual of [(1231, 4), 4851, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(373, 1232, F3, 4, 15) (dual of [(1232, 4), 4855, 16]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(373, 1232, F3, 15) (dual of [1232, 1159, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(373, 2205, F3, 15) (dual of [2205, 2132, 16]-code), using
- 1 times code embedding in larger space [i] based on linear OA(372, 2204, F3, 15) (dual of [2204, 2132, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(371, 2188, F3, 15) (dual of [2188, 2117, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(357, 2188, F3, 13) (dual of [2188, 2131, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(372, 2204, F3, 15) (dual of [2204, 2132, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(373, 2205, F3, 15) (dual of [2205, 2132, 16]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(373, 1232, F3, 15) (dual of [1232, 1159, 16]-code), using
- discarding factors / shortening the dual code based on linear OOA(373, 1232, F3, 4, 15) (dual of [(1232, 4), 4855, 16]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.